{"id":2117,"date":"2011-02-09T00:37:45","date_gmt":"2011-02-08T22:37:45","guid":{"rendered":"http:\/\/laaventuradelasmatematicas.jesussoto.es\/?p=2117"},"modified":"2011-02-09T00:37:45","modified_gmt":"2011-02-08T22:37:45","slug":"particiones-de-un-numero","status":"publish","type":"post","link":"https:\/\/pimedios.jesussoto.es\/?p=2117","title":{"rendered":"Particiones de un n\u00famero"},"content":{"rendered":"<p><a href=\"http:\/\/laaventuradelasmatematicas.jesussoto.es\/wp-content\/uploads\/2011\/02\/ramanujan.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2119\" title=\"ramanujan\" src=\"http:\/\/laaventuradelasmatematicas.jesussoto.es\/wp-content\/uploads\/2011\/02\/ramanujan-236x300.jpg\" alt=\"Contemplating partition (Image: Konrad Jacobs\/Oberwolfach Photo Collection)\" width=\"236\" height=\"300\" \/><\/a>Este problema busca encontrar de cuantas formas diferentes podemos expresar un n\u00famero natural como suma de otros naturales. Parece un planteamiento sencillo, y lo es cuando los n\u00fameros son peque\u00f1os. Por\u00a0ejemplo,\u00a04\u00a0=\u00a03 +1\u00a0=\u00a02 +2\u00a0=\u00a02\u00a0+1 +1\u00a0=\u00a01 +1\u00a0+1 +1,\u00a0por lo que el\u00a0n\u00famero de\u00a0particiones de\u00a04 es 5. Ahora, el n\u00famero de particiones de 10\u00a0es\u00a042, y 100\u00a0tiene m\u00e1s\u00a0de 190 millones de particiones.<\/p>\n<p>Srinivasa Ramanujan estudi\u00f3 este problema y encontr\u00f3 una aproximaci\u00f3n mediante una f\u00f3rmula, que Hardy y Litlewood intentaron simplificar, public\u00e1ndola como Hardy-Litlewood-Ramanujan:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2118 aligncenter\" title=\"paririon\" src=\"http:\/\/laaventuradelasmatematicas.jesussoto.es\/wp-content\/uploads\/2011\/02\/paririon-300x51.png\" alt=\"\" width=\"300\" height=\"51\" \/><\/p>\n<p>Pues bien, en\u00a0un esfuerzo de\u00a0colaboraci\u00f3n\u00a0patrocinado\u00a0por el Instituto Americano\u00a0de Matem\u00e1ticas\u00a0y\u00a0de la\u00a0National Science\u00a0Foundation, un\u00a0equipo\u00a0de\u00a0matem\u00e1ticos dirigido\u00a0por\u00a0Ken\u00a0Ono ha desarrollado nuevas t\u00e9cnicas para\u00a0explorar la\u00a0naturaleza de\u00a0los n\u00fameros\u00a0de particiones.\u00a0\u00abHemos demostrado\u00a0que el n\u00famero de\u00a0particiones son\u00a0&#8216;fractal&#8217;\u00a0para cada primo.\u00a0Nuestro\u00a0&#8216;acercamiento&#8217; resuelve varias conjeturas abiertas\u00bb, dice  Ono.<\/p>\n<p>Ha espera de entender un poco mejor esta noticia, se me abren m\u00e1s interrogantes: \u00bfque es un &#8216;fractal&#8217; para cada primo? (En aimth.org, Frank Calegari has provided a\u00a0<a href=\"http:\/\/www.math.northwestern.edu\/~fcale\/Files\/FKO.pdf\">shorter proof<\/a> of the \u00abfractal\u00bb (<em>l<\/em>-adic) structure of partitions found in Folsom-Kent-Ono.)<\/p>\n<h3>Enlaces de inter\u00e9s<\/h3>\n<ul>\n<li><a href=\"http:\/\/goo.gl\/QLh6I\">Deep meaning in Ramanujan&#8217;s &#8216;simple&#8217; pattern<\/a><\/li>\n<li>The papers\u00a0<a href=\"http:\/\/aimath.org\/news\/partition\/folsom-kent-ono.pdf\">Folsom-Kent-Ono<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Este problema busca encontrar de cuantas formas diferentes podemos expresar un n\u00famero natural como suma de otros naturales. Parece un planteamiento sencillo, y lo es cuando los n\u00fameros son peque\u00f1os. Por\u00a0ejemplo,\u00a04\u00a0=\u00a03 +1\u00a0=\u00a02 +2\u00a0=\u00a02\u00a0+1 +1\u00a0=\u00a01 +1\u00a0+1 +1,\u00a0por lo que el\u00a0n\u00famero de\u00a0particiones de\u00a04 es 5. Ahora, el n\u00famero de particiones de 10\u00a0es\u00a042, y 100\u00a0tiene m\u00e1s\u00a0de 190 millones&hellip; <a class=\"more-link\" href=\"https:\/\/pimedios.jesussoto.es\/?p=2117\">Seguir leyendo <span class=\"screen-reader-text\">Particiones de un n\u00famero<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[166,214,284,302],"class_list":["post-2117","post","type-post","status-publish","format-standard","hentry","category-actualidad","tag-hardy","tag-litlewood","tag-particiones","tag-ramanujan","entry"],"_links":{"self":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/2117","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2117"}],"version-history":[{"count":0,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/2117\/revisions"}],"wp:attachment":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2117"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2117"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2117"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}